Abstract
Many problems of classical mechanics are variational in nature, but not convex. This paper shows how the duality theory of convex optimization can be extended to classical mechanics. It is shown in particular that there is a duality theory for functions of square matrices which factor through the determinant.
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References
Haim Brezis, Jean-Michel Coron, Louis Nirenberg, “Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz”, Comm. Pure Applied Math. 33 (1980), 667–684.
Ivar Ekeland, “Convexity methods in Hamiltonian mechanics”, Springer-Verlag.
Ivar Ekeland, “Le meilleur des mondes possibles”, Seuil; English translation, “The best of all possible worlds” to appear at Chicago University Press.
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© 2004 Springer Science+Business Media New York
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Ekeland, I. (2004). Non-Convex Duality. In: Complementarity, Duality and Symmetry in Nonlinear Mechanics. Advances in Mechanics and Mathematics, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9577-0_2
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DOI: https://doi.org/10.1007/978-90-481-9577-0_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-7119-7
Online ISBN: 978-90-481-9577-0
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